You are standing in air and are looking at a flat piece of glass ( n = 1.52) on

Question

You are standing in air and are looking at a flat piece of glass (n = 1.52) on which there is a layer of transparent plastic (n = 1.61). Light whose wavelength is 542 nm in vacuum is incident nearly perpendicularly on the coated glass and reflects into your eyes. The layer of plastic looks dark. Find the two smallest possible nonzero values for the thickness of the layer. smaller value     nm larger value     nm You are standing in air and are looking at a flat piece of glass (n = 1.52) on which there is a layer of transparent plastic (n = 1.61). Light whose wavelength is 542 nm in vacuum is incident nearly perpendicularly on the coated glass and reflects into your eyes. The layer of plastic looks dark. Find the two smallest possible nonzero values for the thickness of the layer. smaller value     nm larger value     nm (n = 1.52) (n = 1.61). smaller value     nm larger value     nm

Explanation / Answer

the reflection at the top of the sandwich is out of phase
at the bottom it is in phase
so the path difference must be a multiple of whole wavelengths for destructive interference
the wavelength in the plastic is 542/1.52 = 356.57nm
so
1 lambda path difference/2 = thickness = 356.57/2 = 178.28 nm
2 lambda ----> 356.57 nm

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